Problem: Divide the following complex numbers: $\dfrac{9 e^{\pi i}}{3 e^{5\pi i / 12}}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Answer: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $9 e^{\pi i}$ ) has angle $\pi$ and radius 9. The second number ( $3 e^{5\pi i / 12}$ ) has angle $\frac{5}{12}\pi$ and radius 3. The radius of the result will be $\frac{9}{3}$ , which is 3. The angle of the result is $\pi - \frac{5}{12}\pi = \frac{7}{12}\pi$ The radius of the result is $3$ and the angle of the result is $\frac{7}{12}\pi$.